Question

which number line represents the solution to the inequality 2k - 4 ≥ -22 ?

Explanation:

Step1: Solve the inequality \(2k - 4 \geq -22\)

Add 4 to both sides: \(2k - 4 + 4 \geq -22 + 4\)
Simplify: \(2k \geq -18\)

Step2: Divide both sides by 2

\(\frac{2k}{2} \geq \frac{-18}{2}\)
Simplify: \(k \geq -9\)

Now, analyze the number lines:

• Line A: Seems to represent a range less than -9 (incorrect)
• Line B: Represents \(k \geq -7\) (incorrect)
• Line C: Open circle at -9 (incorrect, since we have \(\geq\), should be closed circle) Wait, maybe misread. Wait, looking at the lines: Wait, maybe the labels. Wait, the correct solution is \(k \geq -9\), so the number line with a closed circle at -9 and shading to the right. Looking at the options, D has a closed circle at -9 and shading right? Wait, no, let's recheck. Wait, the original problem's lines: Let's see, line D: closed circle at -9, shading right. Wait, maybe I mislabeled. Wait, the inequality solution is \(k \geq -9\), so the number line should have a closed circle at -9 (since \(\geq\)) and arrow to the right (since \(k\) is greater or equal). So the correct line is D? Wait, no, let's re-express. Wait, the steps:

Wait, solving \(2k - 4 \geq -22\):

1. Add 4: \(2k \geq -18\)
2. Divide by 2: \(k \geq -9\)

So the number line with closed circle at -9, shading to the right (since \(k\) is greater than or equal to -9). Looking at the options, line D has closed circle at -9 and shading right. Wait, but the labels: A, B, C, D. Wait, maybe the initial analysis was wrong. Wait, let's check the lines again.

Wait, line D: closed circle at -9, arrow right. So that's the correct representation.

Answer:

D (with closed circle at -9 and shading to the right, representing \(k \geq -9\))